For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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1answer
44 views

What are some ways to check if a the information given is enough to solve a problem related to euclidean geometry? [closed]

To know if a the data given produces a unique answer is something important because if you know the data is insufficient to yield a unique answer you can stop looking for one. Example: $\triangle ...
0
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0answers
31 views

Recommend guide book of algebraic geometry [duplicate]

I have a little knowledge about geometry and algebraic topology . I want to learn some basic conception and thought of algebraic geometry. Besides , I want to know main of theory of sheaves. What book ...
3
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2answers
96 views

Geometrical Interpretation of Tensors (intuition)

How would one describe to a non-mathematician (an undergraduate physicist actually- so please do use mathematics-i am not even sure if they can be described without mathematics!) what do tensors ...
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0answers
25 views

How do i compute how much i can rotate my tool?

I am at moment trying to implement an Ball tracker for a robot arm with a stereo camera monted on it as its tool. Illustration: http://m.imgur.com/5oojXdh The camera provide me with an dx, dy, dz ...
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1answer
35 views

Find the other 2 interior angles of pentagon inscribed in a circle given 3 angles.

Given a pentagon $ABCDE$ inscribed in a circle with centre $O$. Three of the interior angles are $95^°$, $130^°$ and $138^°$. Find angle $x$ and $y$. I'm quite sure that $x$ and $y$ can be found as ...
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1answer
71 views

How to find the correct value of pi? [duplicate]

Pi is defined as the ratio of $\frac{c}{r}$. Many ancient scintist try to find the value of pi. Some of the values are $\frac{22}{7}$(good hold upto 10 decimal point), $\frac{355}{113}$ (good hold ...
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1answer
15 views

Construction of an $n$-Sphere

I have been thinking about various ways to construct an $n$-sphere. Starting with $S^2$, we can construct it by taking two disks, lifting the "meat" of the disks into a third dimension and then ...
3
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1answer
59 views

Why does $\left(\frac b2\right)^2$ "geometrically complete the square?

I was just reading this MathisFun article on completing the square. It states that geometry can help complete the square. It starts off with a square and a rectangle (pictures come from link): ...
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1answer
25 views

Intersecting three rays and a sphere of known radius

So I actually solved this problem using an iterative solver, but it annoys me because as far as I can tell it should be possible to do it directly. I have three known 3D "rays" that all start at the ...
2
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2answers
67 views

How to solve this geometry problem which involves triangles and triangulation

I need to solve this trig problem. Can you please help me? Based on this image: I need to calculate $PO$ based on the values of $\alpha$, $\beta$ and $AB$ ( Assume that I know the values of ...
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1answer
38 views

Computing the Manhattan Distance between two clusters of points. [closed]

We have two clusters of points: c1: (1, 1), (1, 2), (1, 3) c2: (2, 7), (2, 8), (2, 9) I know the Manhattan Distance formula is as follows: $d(a,b) = \sum|b_i - ...
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1answer
77 views

Prove that $R_1+R_2+R_3=R+r$,where $R$ is the circumradius and $r$ is the inradius of $\triangle ABC.$

Consider a triangle $DEF$,the pedal triangle of the triangle $ABC$ such that $A-F-B$ and $B-D-C$ are collinear.If $H$ is the incenter of $\triangle DEF$ and $R_1,R_2,R_3$ are the circumradii of the ...
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1answer
56 views

Prove that $2A+A_0=A_1+A_2+A_3$,where $A$ is the area of the triangle $ABC.$

If $A_0$ denotes the area of the triangle formed by joining the points of contact of the inscribed circle of the triangle $ABC$ and the sides of the triangle;$A_1,A_2,A_3$ are the corresponding areas ...
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1answer
19 views

Prove that there is at least one acute triangle from 5 segments, each 3 of them form a triangle

I found the following problem - there are 5 segments given. Each three of them can be used to form a valid triangle. I need to prove that there is at least one acute triangle among all possible ...
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1answer
19 views

Decompose any real square matrix in geometrically interpretable matrices

Is it possible to decompose any real square matrix in a product of simple linear maps such as shear, reflection, squeeze, scale and rotation? I think that would provide great insights about the ...
0
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1answer
26 views

What is the length of the shorter trisector of the right angle in a $3$-$4$-$5$ triangle?

What is the length of the shorter trisector of the right angle in a $3$-$4$-$5$ triangle? I found this question in a local question paper, and I am unable to solve it. I applied Cosine formula, ...
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3answers
44 views

geometry - find a point equidistant from three other points

This problem appears in a contest. Can anyone tell me what is the quickest way to solve the problem? Time is a key factor in solving this problem. Thank you very much! Problem: Find the coordinates ...
2
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0answers
15 views

Number of simplices of convex hull of points on a $d$-sphere.

I was discussing this with my professor the other day and he left me to figure out. And I can't for the life of me, figure out why this is so. I would appreciate what I should look into rather than an ...
0
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0answers
21 views

What is the largest perimeter of a convex set with given area and radius? [closed]

Just a thing I was pondering: Take a convex shape in the plane with area A, perimeter P, and contained in a closed ball of radius R. My conjecture is: $$P^{3} \leq 108AR$$ With equality achieved if ...
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0answers
7 views

Building a convex set out of two convex sets where each extremal point of one set shares and edge with each extremal point of the other [duplicate]

Consider a convex set $P$ with two faces $f_1, f_2$ s.t. all extreme points of the convex set belong to either $f_1$ or $f_2$ (but none blong to both - the two faces are disjoint in the set of ...
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4answers
48 views

Geometry Problem. [closed]

ABCD is a square. Parallel lines m, n, and p pass through vertices A, B, and C, respectively. The distance between m and n is 12, and the distance between n and p is 17. Find the area of square ABCD.
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1answer
29 views

Two triangles in a plane

Let $\Delta_1$ and $\Delta_2$ be two triangles in a plane with centroids $G_1$ and $G_2$ respectively. Let $X$, $Y$ be variable points on the perimeter of the triangles $\Delta_1$,$\Delta_2$ ...
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2answers
44 views

If $r$ is the inradius of $\triangle ABC$,then prove that $\frac{2}{r}=\frac{1}{r_a}+\frac{1}{r_b}+\frac{1}{r_c}$

In acute angled triangle $ABC$,a semicircle with radius $r_a$ is constructed with its base on $BC$ and tangent to the other two sides.$r_b$ and $r_c$ are defined similarly.If $r$ is the inradius of ...
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0answers
13 views

How to derive the five-segment axiom of Tarski's geometry from Hilbert's axioms?

We are trying to prove that in an arbitrary Hilbert plane (assuming Hilbert's axioms of Group I:Incidence, II:Order and III:Congruence https://en.wikipedia.org/wiki/Hilbert%27s_axioms), Tarski's ...
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1answer
41 views

Prove that $DQ \times DB = DP \times DC + DR \times DA$.

Let $ABCD$ be a parallelogram, with $P$, $Q$, and $R$ the points on which a given circle passes through $D$ and cuts through the segments $CD$, $BD$ and $AD$ respectively: How do you prove that $DQ ...
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0answers
17 views

If point (cos(theta),sin(theta)) does not fall in the angle btw the lines y=|x-1| in which the origin lies then find the interval which theta belong

I don't get what is the condition for a point to lie between acute or obtuse angled region of two intersecting lines
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3answers
19 views

Geometry, Intersection of Spheres

Can someone explain why the intersection of the unit sphere centred at (0,0,0) an the unit sphere centred at (1,0,0) is a circle of radius $\frac{\sqrt3}{2}$ in the plane {$x_1$=1/2}, centred at ...
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1answer
12 views

Is the simplicial join of two spherical simplicial complexes itself spherical?

I think this ought to be true, but I am struggling to see why. Of course if one of the spheres is $S^0$ then this is trivially true, as we are just glueing two cones along their boundary. I'm not ...
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0answers
24 views

Area of “tubular” neighbourhood of a curve

Assume $\gamma$ is a $C^1$ curve $\gamma: [0,\epsilon]\rightarrow U\subset \mathbb{R}^2$ which is tangent to a continuous non-vanishing vector field $X=\frac{\partial}{\partial x} + ...
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2answers
89 views

Help with complex numbers geometry proof

See this link. The last step is skipped, because it is claimed to be trivial, but apparently there is a gap in my knowledge. $M$ is $\frac{1}{2}(b+c)$ and $H$ is $\frac{1}{2}i(b+c)$, but how do you ...
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0answers
15 views

How do I prove this simple result for the face structure of convex sets?

I have a convex set $P$ with faces $f_1, f_2$ such that all extremal points of the convex set belong to either $f_1$ or $f_2$ (the faces are disjoint and cover $P$). How can I prove that if every ...
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1answer
16 views

Angle of rotation based on apparent change in size

I have a camera set up which views an object in 2D in front of it square on that's 309mm away, the object changes in size by 0.073mm. What I am trying to calculate is by what angle has the object to ...
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0answers
24 views

Cutting cheese into chunks [duplicate]

Into how many chunks can one cut a round piece of cheese with n straight cuts? Consider the $3D$ version My try: f(x) = number of pieces and $'x'$ as number of cuts. $f(1)=2$ $f(2)= 2 + f(1)$ ...
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2answers
28 views

How many square feet a FooFoo can wander?

Can anyone help with this? I got a wrong answer. Problem: Joe's French poodle, FooFoo, is tied to the corner of the barn which measures 40 x 30. FooFoo's rope is 50 long. In terms of π, over how ...
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1answer
23 views

Calculate the radius of a circle given a segment's height and area

Basically I need to know if there is an non-iterative solution to find the radius of a circle when the segment's area and height are known.
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2answers
32 views

Transforming integral in cylindrical coordinates into cartesian.

I am trying to transform the following integral to an integral in cartesian coordinates. $$\int^{2\pi}_0\int^1_0\int^{\sqrt{1-r^2}}_0r \ dzdrd\theta$$ I cannot really visualise how the region enclosed ...
2
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1answer
30 views

Prove that the center of a circle within a constructed triangles lies on the angle bisector

I was given steps to construct a figure: 1.) Construct a horizontal ray AB and a segment AC at an angle to the ray. Locate point D anywhere on ray AB and construct the segment CD. 2.) Construct the ...
0
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1answer
27 views

Two coordinates, two angles, and the third coordinate

Let $A$, $B$ and $C$ be points on a two-dimensional coordinate system. Assume $A=(0,1), B=(0,5)$, angle $\alpha$ of $A$ is 47 degrees, and angle $\beta$ of $B$ is 80 degrees. Calculate the ...
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0answers
17 views

Proof of exactly two supporting lines to convex figure

Given a convex, closed figure that has nonempty interior in $\mathbb{R}^2$, $K$, and any point $P$ outside of it, exactly two supporting lines can be drawn from $P$ to $K$. I am conjecturing this ...
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1answer
32 views

Difference between Grassmann and Projective space?

I recently read the first few chapters of Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling and I am confused about ...
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2answers
64 views

If three cevians are concurrent at a point and form triangles of equal area, the point is the centroid

Let D,E,F be points on side BC,CA,AB of triangle ABC. The three cevians are concurrent at a point G. The areas of triangles BGD, CGE and AGF are equal. Prove that G is the centroid of ABC I ...
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0answers
33 views

Finding the length of circumference using distance between points?

if a sphere is there and two points $(x, y)$ , $(x+dx, y+dy)$ lie on it [$dx, dy$ are infinitesimally small] Now the straight line distance between the two points is $$ds=\sqrt{(dx)^2+(dy)}$$ using ...
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1answer
23 views

Tangent makes with the x-axis

A curve has equation $y=\frac{4}{3x-4}$ and $P$(2,2) is a point on the curve. Find the angle that this tangent makes with the x-axis. Can anyone explain this ?
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0answers
17 views

Can we use contour integral to compute Fourier Transform to reach a better accuracy numerically?

The problem is evaluate the integrals as follows: $$L(t)=\int_{0}^\infty [a(\omega)-a_\infty]\cos(\omega t)d\omega \quad(1)$$ and $$L(t)=\int_{0}^\infty b(\omega)\frac{\sin\omega ...
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5answers
988 views

How many faces of a solid can one “see”?

What is the maximum number of faces of totally convex solid that one can "see" from a point? ...and, more importantly, how can I ask this question better? (I'm a college student with little ...
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1answer
28 views

$A(1,1,1)$, $B(2,1,2)$, $C(3,2,1)$ and $D(2,3,2)$ form a tetrahedron. If $ABC$ is the base, then what is the height?

$A(1,1,1)$, $B(2,1,2)$, $C(3,2,1)$ and $D(2,3,2)$ form a tetrahedron. If $ABC$ is the base, then what is the height? I found out of the equation of the plane containing A, B and C. It is $$-x + 2y +z ...
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0answers
14 views

Help in finding angles in free body diagram.

I figured that $$\tan^{-1}16/8=36.87^\circ$$ but can't find which property of triangles was used to find $53.13$ degrees and $73.74$ degrees angles.
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1answer
30 views

Moving Line Segment Problem part 2

This question is related to a question I asked a while ago here on math.stackexchange: Moving Line Segment Problem The rules for how the line segment can be moved are the same: The endpoints must ...
3
votes
1answer
37 views

Proving that $P$ and $Q$ are symmetric in the line $XY$.

Let $ABCD$ be a cyclic quadrilateral with diagonals intersecting at $T$. Let $P$ and $Q$ be the projections of $T$ onto $AB$ and $CD$ respectively. Let $X$ and $Y$ be the mid-points of $AD$ and $BC$ ...
2
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1answer
36 views

Finding the envelope of the family $(x-c)^2+y^2=1+c^2$

I have this family of circles: $(x-c)^2+y^2=1+c^2$. I'm to find the envelope of this family. Going by what I know, I write $$F(x,y,c)=(x-c)^2+y^2-1-c^2=x^2-2xc+y^2-1=0.$$ Then, $$\frac{\delta ...